They are basically studying the ionosphere by bouncing various frequencies of radio signals off of it and seeing how it reacts and how radio signals change. The sun interacts with the ionosphere in a similar and much stronger way, but it is inconsistent and harder to measure. This is military backed science because the ionosphere affects radio transmissions and GPS, and studying how the ionosphere fluctuates with solar changes can build more robust communication and navigation systems.

They can also induce low and extremely low frequency waves by bouncing the high frequency beam off the ionosphere, there is really no other way to create these frequencies without unrealistically massive antennas. These can be used to communicate with submarines and potentially map underground structures and mineral deposits. This doesn't reach world wide from the HAARP installation, to do these things in the field you'd need a mobile installation.

It can't change the weather any more than a solar flare can, and its about 10,000 times weaker than the sun's electromagnetic radiation we're all being bathed with right now and every day all day.

I've never been, but the facility is open to the public for tours and all their activities are in the public record.

Don't you see, that's what they WANT you to think, that they're being open, pierce the veil, throw off your shackles, etc. etc.